Remotely detuned receiver coil for high-resolution interventional cardiac magnetic resonance imaging

Introduction Interventional cardiac MRI in the context of the treatment of cardiac arrhythmia requires submillimeter image resolution to precisely characterize the cardiac substrate and guide the catheter-based ablation procedure in real-time. Conventional MRI receiver coils positioned on the thorax provide insufficient signal-to-noise ratio (SNR) and spatial selectivity to satisfy these constraints. Methods A small circular MRI receiver coil was developed and evaluated under different experimental conditions, including high-resolution MRI anatomical and thermometric imaging at 1.5 T. From the perspective of developing a therapeutic MR-compatible catheter equipped with a receiver coil, we also propose alternative remote active detuning techniques of the receiver coil using one or two cables. Theoretical details are presented, as well as simulations and experimental validation. Results Anatomical images of the left ventricle at 170 µm in-plane resolution are provided on ex vivo beating heart from swine using a 2 cm circular receiver coil. Taking advantage of the increase of SNR at its vicinity (up to 35 fold compared to conventional receiver coils), real-time MR-temperature imaging can reach an uncertainty below 0.1°C at the submillimetric spatial resolution. Remote active detuning using two cables has similar decoupling efficiency to conventional on-site decoupling, at the cost of an acceptable decrease in the resulting SNR. Discussion This study shows the potential of small dimension surface coils for minimally invasive therapy of cardiac arrhythmia intraoperatively guided by MRI. The proposed remote decoupling approaches may simplify the construction process and reduce the cost of such single-use devices.

resolution) and 5 min 20 s (300 µm in-plane resolution), respectively.Images were acquired at the same location at two different in-plane resolutions.Numbers on the images indicate the slice number of the acquisition sequence.Inserts show a zoomed view with a small vessel visible at 300 µm in-plane resolution (orange arrow).

Classic Detuning and Coupled Resonators
The blocking circuit is usually considered a parallel resonant circuit with a large impedance at its resonance frequency, efficiently impeding the circulation of current in the receive coil.One may understand detuning more accurately by resorting to the general properties of two coupled resonant circuits.A typical implementation of classic detuning is presented in Figure S3 (A).The system consists of two coupled sub-circuits (the receive coil and the blocking circuit), that resonate at the same frequency, which  0 =  0 /2 is the Larmor frequency.

Figure S3: Circuit analysis of coupled resonators
The circuit is composed of LR the inductance of the receive coil, LD the inductance of the detuning coil, CT the tune capacitance, and CC the coupling capacitance used to couple the two circuits.The current circulation in the high-frequency mode (f+) and its equivalent circuit are depicted in (B) and (C), respectively.Also, (D) and (E) represent the current circulation in the low-frequency mode (f-), and its equivalent circuit, respectively.
It turns out that for the system shown in Figure S3A, there are two resonance modes with two different frequencies given by: where f+ and f-are the two new resonance frequencies, respectively high and low, of the detuned receive coil, LR is the inductance of the receive coil, LD is the inductance of the detuning coil in the blocking circuit, CT is the tune capacitance, and CC is the coupling capacitance used to couple the receive coil to the blocking circuit.In Figure S4, f+ and f-of a typical coil in the detuned state (orange), the single resonance frequency,  0 , of the same coil in the non-detuned state (green), as well as the associated detuning efficiency (DE, red) are depicted.This figure has been obtained using a standard double-loop probe S12 measurement [4], [17].In this article, the offset of the new frequencies from the Larmor frequency is referred to as the detuning offset, defined as DE is related to the detuning offset value.A small DO generally leads to a low DE (inefficient detuning).According to Eq.( 1), the smaller the ratio CC/CT, the larger the detuning offset.Provided that the DO is sufficient (f-and f+, both are sufficiently far from f0), the system represents a high impedance at f0 (like any other resonant system far from its resonance frequency).The current that circulates in the coil during the transmission phase will be considerably reduced.In ordinary cases, by choosing the correct values for LR, LD, CT, and CC, one can obtain a sufficient detuning offset and hence an efficient detuning.

Calculation of resonance frequency of a remotely detuned coil
To calculate the two resonance frequencies of a remotely detuned receive coil consider the circuit shown in Figure S5.There are two modes shown by green and brown arrows where the current of the left sub-loop, iL, and the current of the right sub-loop, iR, circulate in opposite directions.One may write the voltage equation for this circuit that leads to two coupled differential equations and solve the equations to find the two resonance frequencies.A more elegant approach is to assume an alternating voltage and consider the complex impedance of each element.In this way, instead of a differential equation, we obtain an algebraic equation for each mode, the root of which is the resonance frequency of that mode.This approach has been used to obtain the resonance frequencies of two coupled LC circuits (N.H. Fletcher and T. D. Rossing, 'Coupled Vibrating Systems', in The Physics of Musical Instruments, New York, NY: Springer New York, 1998, pp.102-132; Eq. 1 was also derived using this approach), and we exploit it here to get the resonance frequencies of the LC circuit connected to a piece of coaxial cable, Figure S5.The complex impedance of an inductor is , that of a short-end stub is  ℎ =   0  (   ), where  2 = −1, and Z0 is the characteristic impedance of the stub (50 Ohms here), l its length, and v the propagation velocity of the stub.Considering these complex impedances, we write the voltage equation in the left sub-loop for the first mode, in which the iL and iR have opposite phases.
The second equation is obtained by writing the voltage equation in the right sub-loop for the first mode:  2) and (3), we can write: The two resonance frequencies of our circuit are the roots of Eq. ( 4).This equation can be solved either numerically, or by graphical methods.For pedagogical reasons, here, we choose the visual approach.
Either parts of Eq. ( 4) are plotted in Figure S6.

Figure S2 .
Figure S2.Description of the experimental setup for MR-imaging of a beating heart from pig.

Figure S4 :
Figure S4: S12 curves in tuned/detuned conditions and measurement of the Detuning Efficiency (DE) and Detuning Offset (DO)

Figure S5 :
Figure S5: Schematic diagram to illustrate the calculations of the two resonance frequencies of a remotely detuned receive coil.Two modes correspond to different directions of current circulation.Each mode corresponds to a different resonance frequency.